Thank you for your response, I appreciate the advice. I am a little worried about the extra time that the bus takes, with the 2 children possibly losing patience and annoying other people around us.
What do you think about hiring a car to self-drive Kyoto to Takayama and then Takayama to Hakone? I found a company that will hire us a medium sized car for about Y32765 for 3 1/2 days, including the fee for dropping the car off in Hakone. We have driven in Thailand, the UK and Malaysia before but I'm not sure how the experience in Japan would compare. I'm also nto sure what teh road from Nagoya to Takayama would be like. Does it possibly become closed due to snow? If this happens, does the train still operate?
Any other advice and info you can offer is greatly appreciated, thanks!